A superconducting solenoid is the most important component of a suspension for overhead transportation facilities operating on the repulsion principle. Its design is aimed at producing an adequate magnetic field within the active zone, to ensure a high ratio of lifting force to braking force, the necessary speed dependence of both forces, and a high ratio of lifting force to solenoid mass. The design must also be both technologically and economically feasible. For safety considerations, the magnetic field intensity inside the passenger compartment must be minimum. A survey of existing designs indicates a preference for race track solenoids of quasi-rectangular shape. While all designers already agree on a coil width within 0.25 to 0.6 m, the optimum coil length has not yet been established. Intrinsic stabilization of superconductors by stranding and twisting has pushed the maximum allowable current density to 200 A/mm/sup 2/ and the energy storing capacity of magnets to 100 kJ, a capacity of 1 MJ being within reach. The recommended coil dimensions for laboratory models are 1 m length and 0.3 m width, to carry magnetizing currents up to 0.3 MA.